Inversion of Hyperpolarized 13C NMR Signals through Cross-Correlated Cross-Relaxation in Dissolution DNP Experiments

Dissolution dynamic nuclear polarization (DDNP) is a versatile tool to boost signal amplitudes in solution-state nuclear magnetic resonance (NMR) spectroscopy. For DDNP, nuclei are spin-hyperpolarized “ex situ” in a dedicated DNP device and then transferred to an NMR spectrometer for detection. Dramatic signal enhancements can be achieved, enabling shorter acquisition times, real-time monitoring of fast reactions, and reduced sample concentrations. Here, we show how the sample transfer in DDNP experiments can affect NMR spectra through cross-correlated cross-relaxation (CCR), especially in the case of low-field passages. Such processes can selectively invert signals of 13C spins in proton-carrying moieties. For their investigations, we use schemes for simultaneous or “parallel” detection of hyperpolarized 1H and 13C nuclei. We find that 1H → 13C CCR can invert signals of 13C spins if the proton polarization is close to 100%. We deduce that low-field passage in a DDNP experiment, a common occurrence due to the introduction of so-called “ultra-shielded” magnets, accelerates these effects due to field-dependent paramagnetic relaxation enhancements that can influence CCR. The reported effects are demonstrated for various molecules, laboratory layouts, and DDNP systems. As coupled 13C–1H spin systems are ubiquitous, we expect similar effects to be observed in various DDNP experiments. This might be exploited for selective spectroscopic labeling of hydrocarbons.

. Simulations of methyl group relaxation starting from -1:-0.01:3 ( 1 H Z : 13 C Z :A-E) order for individual carbon transitions. As indicated in each panel, different relaxation mechanisms were neglected in the simulations. Obviously, a lack of DD relaxation leads to only very weak transfer from the 1 H nuclei to the 13 C nucleus. Figure S2. Influence of the A-E imbalance on the 1 H-13 C CCR starting from -1:-0.01:x ( 1 H Z : 13 C Z :A-E), the value for x is shown at the top of each panel. Figure S3. Representation of the polarization used to simulate the methyl 13 C time traces in the main text. Figure S4. Simulated methyl 1 H longitudinal relaxation time at various magnetic fields switches starting from 6,7 T and considering DD, CSA, DDCSA and rnd mechanisms, but no paramagnetic relaxation enhancement.

Simulations of CH 3 and CH 2 Relaxation.
The signal evolutions (main text Fig. 3 and 4, SI Fig. S1 and S2) were simulated using a modified version of SpinDynamica notebook of reference 1 and runs with Mathematica 12.0 and SpinDynamica 3.5.0.
The relaxation superoperator was generated using Redfield's theory of relaxation by dipolar coupling (DD), chemical shift anisotropy (CSA) and random field fluctuations (rnd): For the first three terms we modeled the systems as rigid rotors using the following formula: Where ι and ι' indices refer either to the atoms involved in case of CSA, or the pair of atoms in case of DD interaction, is the correlation time, is the rotation time, is a Wigner-D matrix element, are the angle between the interaction and the molecular frame, are the irreducible spherical tensors, and are the interaction coefficients. Note that the DD-CSA term in eq. S1 accounts for DD-CSA crosscorrelated cross relaxation, while the DD-DD and CSA-CSA terms account for both cross-correlated as well as auto-relaxation.
The term accounting for random field fluctuations is given by: Where indicates the statistical random field fluctuation at the position of the spin. We considered all the fluctuation correlated for each couple ι ι'. We considered a fluctuation of 30000π 1/s for the proton and 22000π 1/s for carbons.
The relaxation behavior of the spin system was then computed by solving the master equation in Liouville space (see Bengs et al. 2

):
Where  is the density matrix and L the Liouvillian.
The time traces of Fig. S2 were calculated by selectively removing a term from eq. S1.